sin x = 1/3; Find cos x

Draw a right angled triangle

put x as an acute angle and mark th opposite side 1 and the hypotenuse as 3

find the other side using pythagoras theorum.

read off cosx

Actually, there are two solutions.

You can use equation:

sin(x)^2 + cos(x)^2 = 1

Just solve cos(x).

Well there is an infinit number of solutions if there are no restrictions on the domain.

There is one in the first  quad and one in the second quad but you can add 360n degrees or 2npi radians 

where n is any integer.